Date: Nov 17, 2012 11:55 PM
Author: Graham Cooper
Subject: Re: A HARD FLAW in Godel's Proof
On Nov 18, 1:10 pm, "INFINITY POWER" <infin...@limited.com> wrote:

> THINKING CAPS ON!

> ARGUE LOGICALLY!

> ASSUME ANYTHING!

> ROLLBACK ASSUMPTIONS LATER ON <<!

>

> STEP 1: DEFINE a 2 parameter predicate DERIVE(THEOREM, DERIVATION)

>

> DERIVE(T,D) is TRUE IFF

> D contains a sequence of inference rules and substitutions

> and the final formula T in D is logically implied from the Axioms.

>

> - - - - - - - - - - - - - -

>

> STEP 2: DEFINE a Godel Statement.

>

> i.e. Godel Statement named G =

> ALL(M) ~DERIVE(G,M)

>

> - - - - - - - - - - - - - -

>

> STEP 3: IS G A THEOREM?

>

> ASSUME: YES G IS A THEOREM

> DERIVE( G:ALL(M)~DERIVE(G,M) , D )

>

> - - - - - - - - - - - - - -

>

> STEP 4: UNIFY THE QUERY TO THE AXIOMS TO GET THE ANSWER

>

> GOAL : DERIVE( G:ALL(M)~DERIVE(G,M) , D )

> SUBGOAL : G:ALL(M)~DERIVE(G,M)

>

> (SUBGOALs are a Derivation Process that calculate reverse D in the trace)

>

> - - - - - - - - - - - - - - -

>

> STEP 5: REMOVE THE QUANTIFIER

>

> G:~EXIST(M)DERIVE(G,M)

> G: ~DERIVE(G,M)

>

> M is a variable and Existential by Double Variable Instantiation Rule of

> UNIFY().

>

> - - - - - - - - - - - - - - -

>

INSERT A STEP:

STEP 6a

G: ~DERIVE(G, [G | M] )

G is the HEAD of M by definition. (either 1st or last element)

M are the REMAINING TAIL of deductions back to the axioms.

[G <- <M>]

[G <- N <- <O>]

...

[G <- N <- P <- ... <- AXIOMS ]

Now M is strictly FREE as it doesn't contain G as an element in it's

deduction list.

and 6a reduces to 6 below.

>

> STEP 6: M IS A FREE VARIABLE

>

> G: ~DERIVE(G,M)

>

> is a null statement that will return

>

> SUBGOAL: M?

>

> i.e. When parsed by a clever logic compiler, Godel's Statement will return a

> Query in response

>

> [PROVER]- "Why is sentence G not derivable?"

>

> Herc

>

> --

> if( if(t(S),f(R)) , if(t(R),f(S)) ).

> if it's sunny then it's not raining

> ergo

> if it's raining then it's not sunny